This document provides an introduction to deep learning. It discusses how deep learning uses multiple layers of nonlinear processing to automatically extract features from data, avoiding the need for manual feature engineering. Deep belief networks, which are composed of stacked restricted Boltzmann machines, are a widely used deep learning model. Training deep networks is challenging, but this is addressed by an unsupervised layer-wise pretraining approach followed by supervised fine-tuning of the entire network. The document reviews literature on deep learning models and applications.
From RNN to neural networks for cyclic undirected graphstuxette
This document discusses different neural network methods for processing graph-structured data. It begins by describing recurrent neural networks (RNNs) and their limitations for graphs, such as an inability to handle undirected or cyclic graphs. It then summarizes two alternative approaches: one that uses contraction maps to allow recurrent updates on arbitrary graphs, and one that employs a constructive architecture with frozen neurons to avoid issues with cycles. Both methods aim to make predictions at the node or graph level on relational data like molecules or web pages.
The document summarizes an algorithm for image encryption and compression based on compressive sensing and chaos. It begins with background information on compressive sensing theory and multi-chaotic based image encryption. It then describes the proposed algorithm which uses compressive sensing and a multi-chaotic system together for both image encryption and compression in a single step. Simulation results showed that the encrypted images had a large key space, low storage and transmission requirements, high security, and good statistical properties. Recovered images also had good quality while preserving image characteristics.
(DL輪読)Matching Networks for One Shot LearningMasahiro Suzuki
1. Matching Networks is a neural network architecture proposed by DeepMind for one-shot learning.
2. The network learns to classify novel examples by comparing them to a small support set of examples, using an attention mechanism to focus on the most relevant support examples.
3. The network is trained using a meta-learning approach, where it learns to learn from small support sets to classify novel examples from classes not seen during training.
Steganographic Scheme Based on Message-Cover matchingIJECEIAES
Steganography is one of the techniques that enter into the field of information security, it is the art of dissimulating data into digital files in an imperceptible way that does not arise the suspicion. In this paper, a steganographic method based on the FaberSchauder discrete wavelet transform is proposed. The embedding of the secret data is performed in Least Significant Bit (LSB) of the integer part of the wavelet coefficients. The secret message is decomposed into pairs of bits, then each pair is transformed into another based on a permutation that allows to obtain the most matches possible between the message and the LSB of the coefficients. To assess the performance of the proposed method, experiments were carried out on a large set of images, and a comparison to prior works is accomplished. Results show a good level of imperceptibility and a good trade-off imperceptibility-capacity compared to literature.
Convolutional networks and graph networks through kernelstuxette
This presentation discusses how convolutional kernel networks (CKNs) can be used to model sequential and graph-structured data through kernels defined over sequences and graphs. CKNs define feature maps from substructures like n-mers in sequences and paths in graphs into high-dimensional spaces, which are then approximated to obtain low-dimensional representations that can be used for prediction tasks like classification. This approach is analogous to convolutional neural networks and can be extended to multiple layers. The presentation provides examples showing CKNs achieve good performance on problems involving protein sequences and social networks.
(研究会輪読) Facial Landmark Detection by Deep Multi-task LearningMasahiro Suzuki
The document summarizes a research paper on facial landmark detection using deep multi-task learning. It proposes a Tasks-Constrained Deep Convolutional Network (TCDCN) that uses facial landmark detection as the main task and related auxiliary tasks like pose estimation and attribute inference to improve performance. The TCDCN learns shared representations across tasks using a deep convolutional network. It introduces task-wise early stopping to halt learning on auxiliary tasks that reach optimal performance early to avoid overfitting and improve convergence on the main task of landmark detection. Experimental results showed the proposed approach outperformed existing methods.
An Importance Sampling Approach to Integrate Expert Knowledge When Learning B...NTNU
The introduction of expert knowledge when learning Bayesian Networks from data is known to be an excellent approach to boost the performance of automatic learning methods, specially when the data is scarce. Previous approaches for this problem based on Bayesian statistics introduce the expert knowledge modifying the prior probability distributions. In this study, we propose a new methodology based on Monte Carlo simulation which starts with non-informative priors and requires knowledge from the expert a posteriori, when the simulation ends. We also explore a new Importance Sampling method for Monte Carlo simulation and the definition of new non-informative priors for the structure of the network. All these approaches are experimentally validated with five standard Bayesian networks.
Read more:
http://link.springer.com/chapter/10.1007%2F978-3-642-14049-5_70
This document discusses using repeated simulations of a crisp neural network to obtain quasi-fuzzy weight sets (QFWS) that can be used to initialize fuzzy neural networks. The key points are:
1) A crisp neural network is repeatedly trained on input-output data to model an unknown function. The connection weights change with each simulation.
2) Recording the weights from multiple simulations produces quasi-fuzzy weight sets, where each weight is a fuzzy set rather than a single value.
3) These QFWS can provide initial solutions for training type-I fuzzy neural networks with reduced computational complexity compared to random initialization.
4) The QFWS follow fuzzy arithmetic and allow both numerical and linguistic data to
From RNN to neural networks for cyclic undirected graphstuxette
This document discusses different neural network methods for processing graph-structured data. It begins by describing recurrent neural networks (RNNs) and their limitations for graphs, such as an inability to handle undirected or cyclic graphs. It then summarizes two alternative approaches: one that uses contraction maps to allow recurrent updates on arbitrary graphs, and one that employs a constructive architecture with frozen neurons to avoid issues with cycles. Both methods aim to make predictions at the node or graph level on relational data like molecules or web pages.
The document summarizes an algorithm for image encryption and compression based on compressive sensing and chaos. It begins with background information on compressive sensing theory and multi-chaotic based image encryption. It then describes the proposed algorithm which uses compressive sensing and a multi-chaotic system together for both image encryption and compression in a single step. Simulation results showed that the encrypted images had a large key space, low storage and transmission requirements, high security, and good statistical properties. Recovered images also had good quality while preserving image characteristics.
(DL輪読)Matching Networks for One Shot LearningMasahiro Suzuki
1. Matching Networks is a neural network architecture proposed by DeepMind for one-shot learning.
2. The network learns to classify novel examples by comparing them to a small support set of examples, using an attention mechanism to focus on the most relevant support examples.
3. The network is trained using a meta-learning approach, where it learns to learn from small support sets to classify novel examples from classes not seen during training.
Steganographic Scheme Based on Message-Cover matchingIJECEIAES
Steganography is one of the techniques that enter into the field of information security, it is the art of dissimulating data into digital files in an imperceptible way that does not arise the suspicion. In this paper, a steganographic method based on the FaberSchauder discrete wavelet transform is proposed. The embedding of the secret data is performed in Least Significant Bit (LSB) of the integer part of the wavelet coefficients. The secret message is decomposed into pairs of bits, then each pair is transformed into another based on a permutation that allows to obtain the most matches possible between the message and the LSB of the coefficients. To assess the performance of the proposed method, experiments were carried out on a large set of images, and a comparison to prior works is accomplished. Results show a good level of imperceptibility and a good trade-off imperceptibility-capacity compared to literature.
Convolutional networks and graph networks through kernelstuxette
This presentation discusses how convolutional kernel networks (CKNs) can be used to model sequential and graph-structured data through kernels defined over sequences and graphs. CKNs define feature maps from substructures like n-mers in sequences and paths in graphs into high-dimensional spaces, which are then approximated to obtain low-dimensional representations that can be used for prediction tasks like classification. This approach is analogous to convolutional neural networks and can be extended to multiple layers. The presentation provides examples showing CKNs achieve good performance on problems involving protein sequences and social networks.
(研究会輪読) Facial Landmark Detection by Deep Multi-task LearningMasahiro Suzuki
The document summarizes a research paper on facial landmark detection using deep multi-task learning. It proposes a Tasks-Constrained Deep Convolutional Network (TCDCN) that uses facial landmark detection as the main task and related auxiliary tasks like pose estimation and attribute inference to improve performance. The TCDCN learns shared representations across tasks using a deep convolutional network. It introduces task-wise early stopping to halt learning on auxiliary tasks that reach optimal performance early to avoid overfitting and improve convergence on the main task of landmark detection. Experimental results showed the proposed approach outperformed existing methods.
An Importance Sampling Approach to Integrate Expert Knowledge When Learning B...NTNU
The introduction of expert knowledge when learning Bayesian Networks from data is known to be an excellent approach to boost the performance of automatic learning methods, specially when the data is scarce. Previous approaches for this problem based on Bayesian statistics introduce the expert knowledge modifying the prior probability distributions. In this study, we propose a new methodology based on Monte Carlo simulation which starts with non-informative priors and requires knowledge from the expert a posteriori, when the simulation ends. We also explore a new Importance Sampling method for Monte Carlo simulation and the definition of new non-informative priors for the structure of the network. All these approaches are experimentally validated with five standard Bayesian networks.
Read more:
http://link.springer.com/chapter/10.1007%2F978-3-642-14049-5_70
This document discusses using repeated simulations of a crisp neural network to obtain quasi-fuzzy weight sets (QFWS) that can be used to initialize fuzzy neural networks. The key points are:
1) A crisp neural network is repeatedly trained on input-output data to model an unknown function. The connection weights change with each simulation.
2) Recording the weights from multiple simulations produces quasi-fuzzy weight sets, where each weight is a fuzzy set rather than a single value.
3) These QFWS can provide initial solutions for training type-I fuzzy neural networks with reduced computational complexity compared to random initialization.
4) The QFWS follow fuzzy arithmetic and allow both numerical and linguistic data to
This document summarizes kernel methods in machine learning. It begins with an introductory example of using a kernel function to perform binary classification in a reproducing kernel Hilbert space. It then defines positive definite kernels and shows how they allow representing algorithms as operating in linear dot product spaces while using nonlinear kernel functions. The document covers fundamental properties of kernels, provides examples, and discusses how kernels define reproducing kernel Hilbert spaces for regularization. It overviews various kernel-based machine learning approaches and modeling structured responses using statistical models in reproducing kernel Hilbert spaces.
This document discusses parallelizing object detection in videos for many-core systems. It presents an object detection algorithm that includes frame differencing, background differencing, post-processing, and background updating. The algorithm is parallelized by vertically partitioning video frames across cores, with some pixel overlap between partitions to reduce communication overhead. The parallel implementation achieves a speedup of 37.2x on a 64-core Tilera system processing 18 full-HD frames per second. A performance prediction equation is also developed and shown to accurately model the real performance results.
The document discusses machine learning concepts including supervised and unsupervised learning algorithms like clustering, dimensionality reduction, and classification. It also covers parallel computing strategies for machine learning like partitioning problems across distributed memory architectures.
The document discusses character recognition using convolutional neural networks. It begins with an introduction to classifiers and gradient-based learning methods. It then describes how multiple perceptrons can be combined into a multilayer perceptron and trained using backpropagation. Next, it introduces convolutional neural networks, which offer improvements over multilayer perceptrons in performance, accuracy, and distortion invariance. It provides details on the topology and training of convolutional neural networks. Finally, it discusses the LeNet-5 convolutional neural network and its successful application to handwritten digit recognition.
In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on conventional, classical computers. We show that quantum computing not only reduces the time required to train a deep restricted Boltzmann machine, but also provides a richer and more comprehensive framework for deep learning than classical computing and leads to significant improvements in the optimization of the underlying objective function. Our quantum methods also permit efficient training of full Boltzmann machines and multilayer, fully connected models and do not have well known classical counterparts.
This document discusses using fuzzy clustering to group real estate properties. It presents a case study clustering 46 real estate listings into 3 groups based on price, area, and region attributes. The fuzzy c-means clustering algorithm in MATLAB is used to assign membership levels and cluster centroids. The results identify 3 clusters - one for mid-priced properties in good regions and average areas, one for high-priced properties in excellent regions and large areas, and one for low-priced properties in poor regions and small areas. Graphs and tables show the clustered properties and centroids.
The mathematician M. Gromov stands among geometers as one of the most original and productive researcher, with unique contributions to the field of geometric group theory. In the recent years, he turned his attention towards the applications of mathematics to neuroscience. His ideas have been collected in a series of articles that form a kind of mathematical diary. In this introductory talk, we will provide some pointers to these texts and work out one example of application of geometric group theory to the large scale structure of neural pathways.
https://telecombcn-dl.github.io/2018-dlai/
Deep learning technologies are at the core of the current revolution in artificial intelligence for multimedia data analysis. The convergence of large-scale annotated datasets and affordable GPU hardware has allowed the training of neural networks for data analysis tasks which were previously addressed with hand-crafted features. Architectures such as convolutional neural networks, recurrent neural networks or Q-nets for reinforcement learning have shaped a brand new scenario in signal processing. This course will cover the basic principles of deep learning from both an algorithmic and computational perspectives.
Kernel methods and variable selection for exploratory analysis and multi-omic...tuxette
Nathalie Vialaneix
4th course on Computational Systems Biology of Cancer: Multi-omics and Machine Learning Approaches
International course, Curie training
https://training.institut-curie.org/courses/sysbiocancer2021
(remote)
September 29th, 2021
The document proposes a method called generalized time warping (GTW) to temporally align multi-modal sequences from multiple subjects performing similar activities. GTW aims to overcome limitations of existing approaches like dynamic time warping (DTW) which have quadratic complexity and cannot easily align multiple sequences. GTW uses multi-set canonical correlation analysis to find spatial transformations between modalities and models the temporal warping as a combination of monotonic basis functions, allowing a more flexible alignment. Experimental results show GTW can efficiently solve multi-modal temporal alignment and outperforms DTW for intra-modality alignment.
This document summarizes a study on pattern recognition and learning in networks of coupled bistable units. The network is composed of N oscillators moving in a double-well potential, with pair-wise interactions between all elements. Two methods are used for training the network: (1) constructing the coupling matrix using Hebb's rule based on stored patterns, and (2) iteratively updating the matrix to minimize error between applied and desired patterns. Graphs show the learning rate converges as mean squared error and coupling strengths decrease over iterations.
Self Organizing Maps (SOMs) are a type of neural network that uses unsupervised learning to map high-dimensional input data to a low-dimensional discrete map. SOMs learn the topological relationships in the training data and organize themselves through competition between neurons to become selectively tuned to different input patterns. The algorithm involves initializing weights, finding a winning neuron for each input, and updating the weights of the winning neuron and its neighbors to more closely match the input. Repeated iterations of this process cause the neurons to self-organize the input space onto the map in a topologically ordered fashion.
Self-Organizing Maps (SOM) are a type of neural network that can be used for clustering and visualizing complex, high-dimensional data. SOM reduces dimensionality while preserving topological relationships. It arranges nodes on a grid such that similar input vectors are mapped to nearby nodes. During training, the best matching node and its neighbors are adjusted to better match the input. This results in a 2D map where similar data clusters together. For example, a SOM was used to cluster countries based on quality of life indicators, grouping those with similar living standards. SOM can be useful for applications like data mining, pattern recognition, and more.
This document discusses various clustering techniques for image segmentation. It begins by defining clustering and image segmentation. It then describes four main clustering techniques - exclusive clustering (e.g. k-means), overlapping clustering (e.g. fuzzy c-means), hierarchical clustering, and probabilistic-D clustering. For each technique, it provides details on the clustering algorithm and steps. It concludes that fuzzy c-means is superior to other approaches for image segmentation efficiency but has high computational time, while probabilistic-D clustering aims to reduce this time.
Using Multi-layered Feed-forward Neural Network (MLFNN) Architecture as Bidir...IOSR Journals
This document presents a method for using a multi-layered feed-forward neural network (MLFNN) architecture as a bidirectional associative memory (BAM) for function approximation. It proposes applying the backpropagation algorithm in two phases - first in the forward direction, then in the backward direction - which allows the MLFNN to work like a BAM. Simulation results show that this two-phase backpropagation algorithm achieves convergence faster than standard backpropagation when approximating the sine function, demonstrating that the MLFNN architecture is better suited for function approximation when trained this way.
MLPfit is a tool for designing and training multi-layer perceptrons (MLPs) for tasks like function approximation and classification. It implements stochastic minimization as well as more powerful methods like conjugate gradients and BFGS. MLPfit is designed to be simple, precise, fast and easy to use for both standalone and integrated applications. Documentation and source code are available online.
Artificial neural networks are computer programs that can recognize patterns in data and produce models to represent that data. They are inspired by the human brain in how knowledge is acquired through learning and stored in the connections between neurons. Neural networks learn by adjusting the strengths of connections between neurons based on examples provided during training. They are able to model and learn both linear and nonlinear relationships in data.
This document contains lecture notes on sparse autoencoders. It begins with an introduction describing the limitations of supervised learning and the need for algorithms that can automatically learn feature representations from unlabeled data. The notes then state that sparse autoencoders are one approach to learn features from unlabeled data, and describe the organization of the rest of the notes. The notes will cover feedforward neural networks, backpropagation for supervised learning, autoencoders for unsupervised learning, and how sparse autoencoders are derived from these concepts.
This document discusses using the Levenberg-Marquardt algorithm for forecasting stock exchange share rates on the Karachi Stock Exchange. It provides an overview of artificial neural networks and how they can be used for financial forecasting applications. The Levenberg-Marquardt algorithm is presented as an efficient method for training neural networks to minimize errors through gradient descent. The document applies this method to train a neural network to predict the direction of change in share prices on the Karachi Stock Exchange. The network is trained on historical stock price data and testing shows it can achieve the performance goal of forecasting next day price changes.
This document presents a method for applying random matrix theory to analyze deep neural networks using nonlinear activations. The key results are:
1) The moments method is used to derive a quartic equation that the Stieltjes transform of the Gram matrix YTY satisfies, where Y=f(WX) and W,X are random matrices and f is a nonlinear activation.
2) This allows computing properties of the Gram matrix like its limiting spectral distribution and the training loss of a random feature network.
3) Certain activations preserve the eigenvalue distribution of the data covariance matrix XTX, analogous to batch normalization. These activations may improve training and are a new class worthy of further study.
Improving Performance of Back propagation Learning Algorithmijsrd.com
The standard back-propagation algorithm is one of the most widely used algorithm for training feed-forward neural networks. One major drawback of this algorithm is it might fall into local minima and slow convergence rate. Natural gradient descent is principal method for solving nonlinear function is presented and is combined with the modified back-propagation algorithm yielding a new fast training multilayer algorithm. This paper describes new approach to natural gradient learning in which the number of parameters necessary is much smaller than the natural gradient algorithm. This new method exploits the algebraic structure of the parameter space to reduce the space and time complexity of algorithm and improve its performance.
This document describes a study using artificial neural networks (ANNs) to model complex nonlinear systems. Specifically, it discusses:
1) Using an ANN to predict pressure distributions on a rotor wing during ramping motion, with results showing accurate prediction of spatial and temporal evolution.
2) Applying the same ANN model to predict performance of a bank stock based on trends in the stock and stock market index.
3) Proposing a framework combining ANNs with mathematical models to obtain better predictions and representations of financial data trends.
This document summarizes kernel methods in machine learning. It begins with an introductory example of using a kernel function to perform binary classification in a reproducing kernel Hilbert space. It then defines positive definite kernels and shows how they allow representing algorithms as operating in linear dot product spaces while using nonlinear kernel functions. The document covers fundamental properties of kernels, provides examples, and discusses how kernels define reproducing kernel Hilbert spaces for regularization. It overviews various kernel-based machine learning approaches and modeling structured responses using statistical models in reproducing kernel Hilbert spaces.
This document discusses parallelizing object detection in videos for many-core systems. It presents an object detection algorithm that includes frame differencing, background differencing, post-processing, and background updating. The algorithm is parallelized by vertically partitioning video frames across cores, with some pixel overlap between partitions to reduce communication overhead. The parallel implementation achieves a speedup of 37.2x on a 64-core Tilera system processing 18 full-HD frames per second. A performance prediction equation is also developed and shown to accurately model the real performance results.
The document discusses machine learning concepts including supervised and unsupervised learning algorithms like clustering, dimensionality reduction, and classification. It also covers parallel computing strategies for machine learning like partitioning problems across distributed memory architectures.
The document discusses character recognition using convolutional neural networks. It begins with an introduction to classifiers and gradient-based learning methods. It then describes how multiple perceptrons can be combined into a multilayer perceptron and trained using backpropagation. Next, it introduces convolutional neural networks, which offer improvements over multilayer perceptrons in performance, accuracy, and distortion invariance. It provides details on the topology and training of convolutional neural networks. Finally, it discusses the LeNet-5 convolutional neural network and its successful application to handwritten digit recognition.
In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on conventional, classical computers. We show that quantum computing not only reduces the time required to train a deep restricted Boltzmann machine, but also provides a richer and more comprehensive framework for deep learning than classical computing and leads to significant improvements in the optimization of the underlying objective function. Our quantum methods also permit efficient training of full Boltzmann machines and multilayer, fully connected models and do not have well known classical counterparts.
This document discusses using fuzzy clustering to group real estate properties. It presents a case study clustering 46 real estate listings into 3 groups based on price, area, and region attributes. The fuzzy c-means clustering algorithm in MATLAB is used to assign membership levels and cluster centroids. The results identify 3 clusters - one for mid-priced properties in good regions and average areas, one for high-priced properties in excellent regions and large areas, and one for low-priced properties in poor regions and small areas. Graphs and tables show the clustered properties and centroids.
The mathematician M. Gromov stands among geometers as one of the most original and productive researcher, with unique contributions to the field of geometric group theory. In the recent years, he turned his attention towards the applications of mathematics to neuroscience. His ideas have been collected in a series of articles that form a kind of mathematical diary. In this introductory talk, we will provide some pointers to these texts and work out one example of application of geometric group theory to the large scale structure of neural pathways.
https://telecombcn-dl.github.io/2018-dlai/
Deep learning technologies are at the core of the current revolution in artificial intelligence for multimedia data analysis. The convergence of large-scale annotated datasets and affordable GPU hardware has allowed the training of neural networks for data analysis tasks which were previously addressed with hand-crafted features. Architectures such as convolutional neural networks, recurrent neural networks or Q-nets for reinforcement learning have shaped a brand new scenario in signal processing. This course will cover the basic principles of deep learning from both an algorithmic and computational perspectives.
Kernel methods and variable selection for exploratory analysis and multi-omic...tuxette
Nathalie Vialaneix
4th course on Computational Systems Biology of Cancer: Multi-omics and Machine Learning Approaches
International course, Curie training
https://training.institut-curie.org/courses/sysbiocancer2021
(remote)
September 29th, 2021
The document proposes a method called generalized time warping (GTW) to temporally align multi-modal sequences from multiple subjects performing similar activities. GTW aims to overcome limitations of existing approaches like dynamic time warping (DTW) which have quadratic complexity and cannot easily align multiple sequences. GTW uses multi-set canonical correlation analysis to find spatial transformations between modalities and models the temporal warping as a combination of monotonic basis functions, allowing a more flexible alignment. Experimental results show GTW can efficiently solve multi-modal temporal alignment and outperforms DTW for intra-modality alignment.
This document summarizes a study on pattern recognition and learning in networks of coupled bistable units. The network is composed of N oscillators moving in a double-well potential, with pair-wise interactions between all elements. Two methods are used for training the network: (1) constructing the coupling matrix using Hebb's rule based on stored patterns, and (2) iteratively updating the matrix to minimize error between applied and desired patterns. Graphs show the learning rate converges as mean squared error and coupling strengths decrease over iterations.
Self Organizing Maps (SOMs) are a type of neural network that uses unsupervised learning to map high-dimensional input data to a low-dimensional discrete map. SOMs learn the topological relationships in the training data and organize themselves through competition between neurons to become selectively tuned to different input patterns. The algorithm involves initializing weights, finding a winning neuron for each input, and updating the weights of the winning neuron and its neighbors to more closely match the input. Repeated iterations of this process cause the neurons to self-organize the input space onto the map in a topologically ordered fashion.
Self-Organizing Maps (SOM) are a type of neural network that can be used for clustering and visualizing complex, high-dimensional data. SOM reduces dimensionality while preserving topological relationships. It arranges nodes on a grid such that similar input vectors are mapped to nearby nodes. During training, the best matching node and its neighbors are adjusted to better match the input. This results in a 2D map where similar data clusters together. For example, a SOM was used to cluster countries based on quality of life indicators, grouping those with similar living standards. SOM can be useful for applications like data mining, pattern recognition, and more.
This document discusses various clustering techniques for image segmentation. It begins by defining clustering and image segmentation. It then describes four main clustering techniques - exclusive clustering (e.g. k-means), overlapping clustering (e.g. fuzzy c-means), hierarchical clustering, and probabilistic-D clustering. For each technique, it provides details on the clustering algorithm and steps. It concludes that fuzzy c-means is superior to other approaches for image segmentation efficiency but has high computational time, while probabilistic-D clustering aims to reduce this time.
Using Multi-layered Feed-forward Neural Network (MLFNN) Architecture as Bidir...IOSR Journals
This document presents a method for using a multi-layered feed-forward neural network (MLFNN) architecture as a bidirectional associative memory (BAM) for function approximation. It proposes applying the backpropagation algorithm in two phases - first in the forward direction, then in the backward direction - which allows the MLFNN to work like a BAM. Simulation results show that this two-phase backpropagation algorithm achieves convergence faster than standard backpropagation when approximating the sine function, demonstrating that the MLFNN architecture is better suited for function approximation when trained this way.
MLPfit is a tool for designing and training multi-layer perceptrons (MLPs) for tasks like function approximation and classification. It implements stochastic minimization as well as more powerful methods like conjugate gradients and BFGS. MLPfit is designed to be simple, precise, fast and easy to use for both standalone and integrated applications. Documentation and source code are available online.
Artificial neural networks are computer programs that can recognize patterns in data and produce models to represent that data. They are inspired by the human brain in how knowledge is acquired through learning and stored in the connections between neurons. Neural networks learn by adjusting the strengths of connections between neurons based on examples provided during training. They are able to model and learn both linear and nonlinear relationships in data.
This document contains lecture notes on sparse autoencoders. It begins with an introduction describing the limitations of supervised learning and the need for algorithms that can automatically learn feature representations from unlabeled data. The notes then state that sparse autoencoders are one approach to learn features from unlabeled data, and describe the organization of the rest of the notes. The notes will cover feedforward neural networks, backpropagation for supervised learning, autoencoders for unsupervised learning, and how sparse autoencoders are derived from these concepts.
This document discusses using the Levenberg-Marquardt algorithm for forecasting stock exchange share rates on the Karachi Stock Exchange. It provides an overview of artificial neural networks and how they can be used for financial forecasting applications. The Levenberg-Marquardt algorithm is presented as an efficient method for training neural networks to minimize errors through gradient descent. The document applies this method to train a neural network to predict the direction of change in share prices on the Karachi Stock Exchange. The network is trained on historical stock price data and testing shows it can achieve the performance goal of forecasting next day price changes.
This document presents a method for applying random matrix theory to analyze deep neural networks using nonlinear activations. The key results are:
1) The moments method is used to derive a quartic equation that the Stieltjes transform of the Gram matrix YTY satisfies, where Y=f(WX) and W,X are random matrices and f is a nonlinear activation.
2) This allows computing properties of the Gram matrix like its limiting spectral distribution and the training loss of a random feature network.
3) Certain activations preserve the eigenvalue distribution of the data covariance matrix XTX, analogous to batch normalization. These activations may improve training and are a new class worthy of further study.
Improving Performance of Back propagation Learning Algorithmijsrd.com
The standard back-propagation algorithm is one of the most widely used algorithm for training feed-forward neural networks. One major drawback of this algorithm is it might fall into local minima and slow convergence rate. Natural gradient descent is principal method for solving nonlinear function is presented and is combined with the modified back-propagation algorithm yielding a new fast training multilayer algorithm. This paper describes new approach to natural gradient learning in which the number of parameters necessary is much smaller than the natural gradient algorithm. This new method exploits the algebraic structure of the parameter space to reduce the space and time complexity of algorithm and improve its performance.
This document describes a study using artificial neural networks (ANNs) to model complex nonlinear systems. Specifically, it discusses:
1) Using an ANN to predict pressure distributions on a rotor wing during ramping motion, with results showing accurate prediction of spatial and temporal evolution.
2) Applying the same ANN model to predict performance of a bank stock based on trends in the stock and stock market index.
3) Proposing a framework combining ANNs with mathematical models to obtain better predictions and representations of financial data trends.
U-Net is a convolutional neural network (CNN) architecture designed for semantic segmentation tasks, especially in the field of medical image analysis. It was introduced by Olaf Ronneberger, Philipp Fischer, and Thomas Brox in 2015. The name "U-Net" comes from its U-shaped architecture.
Key features of the U-Net architecture:
U-Shaped Design: U-Net consists of a contracting path (downsampling) and an expansive path (upsampling). The architecture resembles the letter "U" when visualized.
Contracting Path (Encoder):
The contracting path involves a series of convolutional and pooling layers.
Each convolutional layer is followed by a rectified linear unit (ReLU) activation function and possibly other normalization or activation functions.
Pooling layers (usually max pooling) reduce spatial dimensions, capturing high-level features.
Expansive Path (Decoder):
The expansive path involves a series of upsampling and convolutional layers.
Upsampling is achieved using transposed convolution (also known as deconvolution or convolutional transpose).
Skip connections are established between corresponding layers in the contracting and expansive paths. These connections help retain fine-grained spatial information during the upsampling process.
Skip Connections:
Skip connections concatenate feature maps from the contracting path to the corresponding layers in the expansive path.
These connections facilitate the fusion of low-level and high-level features, aiding in precise localization.
Final Layer:
The final layer typically uses a convolutional layer with a softmax activation function for multi-class segmentation tasks, providing probability scores for each class.
U-Net's architecture and skip connections help address the challenge of segmenting objects with varying sizes and shapes, which is often encountered in medical image analysis. Its success in this domain has led to its application in other areas of computer vision as well.
The U-Net architecture has also been extended and modified in various ways, leading to improvements like the U-Net++ architecture and variations with attention mechanisms, which further enhance the segmentation performance.
U-Net's intuitive design and effectiveness in semantic segmentation tasks have made it a cornerstone in the field of medical image analysis and an influential architecture for researchers working on segmentation challenges.
This document provides an introduction to feedforward neural networks. It discusses two main types: multilayer perceptrons and radial basis function networks. For multilayer perceptrons, it describes supervised learning using the backpropagation algorithm, which involves propagating input data forward through the network and then backpropagating error signals to adjust weights. It also discusses heuristics to improve backpropagation learning and techniques like cross-validation for model selection and stopping training. For radial basis function networks, it notes they differ from multilayer perceptrons in using local rather than global approximation and having a single hidden layer with a linear output layer.
This document provides instructions for three exercises using artificial neural networks (ANNs) in Matlab: function fitting, pattern recognition, and clustering. It begins with background on ANNs including their structure, learning rules, training process, and common architectures. The exercises then guide using ANNs in Matlab for regression to predict house prices from data, classification of tumors as benign or malignant, and clustering of data. Instructions include loading data, creating and training networks, and evaluating results using both the GUI and command line. Improving results through retraining or adding neurons is also discussed.
There are very few examples of the use of various architectures for recurrent neural
networks to predict student learning outcomes. In fact, the only architecture used to
solve this problem is the LSTM architecture. In the works devoted to the use of LSTM
to predict educational outcomes, the results of a detailed theoretical substantiation of
the preference of this particular architecture of the RNN are not presented. In this
regard, it seems advisable to provide such justification in the framework of this study.
The main property of input data for prediction of educational outcomes is its
temporary nature. Some sequence of user actions unfolds in time and is evaluated
(classified) by an external observer as evidence of the presence or absence of an
educational result (objective or metaobjective). In this regard, the RNN used to classify
user actions should perform a procedure for adjusting the weights of neurons for a
certain set of states in the past. At the same time, the length of the sequence of these
states is not predetermined: it can be both short (for example, for objective results),
and quite long.
X-TREPAN: A MULTI CLASS REGRESSION AND ADAPTED EXTRACTION OF COMPREHENSIBLE D...cscpconf
In this work, the TREPAN algorithm is enhanced and extended for extracting decision trees from neural networks. We empirically evaluated the performance of the algorithm on a set of databases from real world events. This benchmark enhancement was achieved by adapting Single-test TREPAN and C4.5 decision tree induction algorithms to analyze the datasets. The models are then compared with X-TREPAN for comprehensibility and classification accuracy. Furthermore, we validate the experimentations by applying statistical methods. Finally, the modified algorithm is extended to work with multi-class regression problems and the ability to comprehend generalized feed forward networks is achieved.
X-TREPAN : A Multi Class Regression and Adapted Extraction of Comprehensible ...csandit
The document describes an algorithm called X-TREPAN that extracts decision trees from trained neural networks. X-TREPAN is an enhancement of the TREPAN algorithm that allows it to handle both multi-class classification and multi-class regression problems. It can also analyze generalized feed forward networks. The algorithm was tested on several real-world datasets and was found to generate decision trees with good classification accuracy while also maintaining comprehensibility.
Drobics, m. 2001: datamining using synergiesbetween self-organising maps and...ArchiLab 7
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This document summarizes a presentation about variational autoencoders (VAEs) presented at the ICLR 2016 conference. The document discusses 5 VAE-related papers presented at ICLR 2016, including Importance Weighted Autoencoders, The Variational Fair Autoencoder, Generating Images from Captions with Attention, Variational Gaussian Process, and Variationally Auto-Encoded Deep Gaussian Processes. It also provides background on variational inference and VAEs, explaining how VAEs use neural networks to model probability distributions and maximize a lower bound on the log likelihood.
TFFN: Two Hidden Layer Feed Forward Network using the randomness of Extreme L...Nimai Chand Das Adhikari
The learning speed of the feed forward neural
network takes a lot of time to be trained which is a major
drawback in their applications since the past decades. The
key reasons behind may be due to the slow gradient-based
learning algorithms which are extensively used to train the
neural networks or due to the parameters in the networks
which are tuned iteratively using some learning algorithms.
Thus, in order to eradicate the above pitfalls, a new learning
algorithm was proposed known as Extreme Learning Machines
(ELM). This algorithm tries to compute Hidden-layer-output
matrix that is made of randomly assigned input layer and
hidden layer weights and randomly assigned biases. Unlike the
other feedforward networks, ELM has the access of the whole
training dataset before going into the computation part. Here,
we have devised a new two-layer-feedforward network (TFFN)
for ELM in a new manner with randomly assigning the weights
and biases in both the hidden layers, which then calculates the
output-hidden layer weights using the Moore-Penrose generalized
inverse. TFFN doesn’t restricts the algorithm to fix the number
of hidden neurons that the algorithm should have. Rather it
searches the space which gives an optimized result in the neurons
combination in both the hidden layers. This algorithm provides a
good generalization capability than the parent Extreme Learning
Machines at an extremely fast learning speed. Here, we have
experimented the algorithm on various types of datasets and
various popular algorithm to find the performances and report
a comparison.
(DL hacks輪読) How to Train Deep Variational Autoencoders and Probabilistic Lad...Masahiro Suzuki
This document discusses techniques for training deep variational autoencoders and probabilistic ladder networks. It proposes three advances: 1) Using an inference model similar to ladder networks with multiple stochastic layers, 2) Adding a warm-up period to keep units active early in training, and 3) Using batch normalization. These advances allow training models with up to five stochastic layers and achieve state-of-the-art log-likelihood results on benchmark datasets. The document explains variational autoencoders, probabilistic ladder networks, and how the proposed techniques parameterize the generative and inference models.
APPLYING NEURAL NETWORKS FOR SUPERVISED LEARNING OF MEDICAL DATAIJDKP
Constructing a classification model based on some given patterns is a form of learning from the environment perception. This modelling aims to discover new knowledge embedded in the input observations. Learning behaviour of the neural network model enhances the classification properties. This paper considers artificial neural networks for learning two different medical data sets in term of number of instances. The experiment results confirm that the back-propagation supervised learning algorithm has proved its efficiency for such non-linear classification issues.
A Learning Linguistic Teaching Control for a Multi-Area Electric Power SystemCSCJournals
This paper presents a new methodology for designing a neuro-fuzzy control for complex physical systems. By developing a Neural -Fuzzy system learning with linguistic teaching signals. The advantage of this technique is that, produce a simple and well-performing system because it selects the fuzzy sets and the numerical numbers and process both numerical and linguistic information. This approach is able to process and learn numerical information as well as linguistic information. The proposed control scheme is applied to a multi-area power system with hydraulic and thermal turbines.
A SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMSIJNSA Journal
The smart irrigation system represents an innovative approach to optimize water usage in agricultural and landscaping practices. The integration of cutting-edge technologies, including sensors, actuators, and data analysis, empowers this system to provide accurate monitoring and control of irrigation processes by leveraging real-time environmental conditions. The main objective of a smart irrigation system is to optimize water efficiency, minimize expenses, and foster the adoption of sustainable water management methods. This paper conducts a systematic risk assessment by exploring the key components/assets and their functionalities in the smart irrigation system. The crucial role of sensors in gathering data on soil moisture, weather patterns, and plant well-being is emphasized in this system. These sensors enable intelligent decision-making in irrigation scheduling and water distribution, leading to enhanced water efficiency and sustainable water management practices. Actuators enable automated control of irrigation devices, ensuring precise and targeted water delivery to plants. Additionally, the paper addresses the potential threat and vulnerabilities associated with smart irrigation systems. It discusses limitations of the system, such as power constraints and computational capabilities, and calculates the potential security risks. The paper suggests possible risk treatment methods for effective secure system operation. In conclusion, the paper emphasizes the significant benefits of implementing smart irrigation systems, including improved water conservation, increased crop yield, and reduced environmental impact. Additionally, based on the security analysis conducted, the paper recommends the implementation of countermeasures and security approaches to address vulnerabilities and ensure the integrity and reliability of the system. By incorporating these measures, smart irrigation technology can revolutionize water management practices in agriculture, promoting sustainability, resource efficiency, and safeguarding against potential security threats.
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Understanding Inductive Bias in Machine LearningSUTEJAS
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Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
1. An Introduction to Deep Learning
Ludovic Arnold1,2
, Sébastien Rebecchi1
, Sylvain Chevallier1
, Hélène Paugam-Moisy1,3
1- Tao, INRIA-Saclay, LRI, UMR8623, Université Paris-Sud 11
F-91405 Orsay, France
2- LIMSI, UMR3251
F-91403 Orsay, France
3- Université Lyon 2, LIRIS, UMR5205
F-69676 Bron, France
Abstract. The deep learning paradigm tackles problems on which shal-
low architectures (e.g. SVM) are affected by the curse of dimensionality.
As part of a two-stage learning scheme involving multiple layers of non-
linear processing a set of statistically robust features is automatically ex-
tracted from the data. The present tutorial introducing the ESANN deep
learning special session details the state-of-the-art models and summarizes
the current understanding of this learning approach which is a reference
for many difficult classification tasks.
1 Introduction
In statistical machine learning, a major issue is the selection of an appropriate
feature space where input instances have desired properties for solving a par-
ticular problem. For example, in the context of supervised learning for binary
classification, it is often required that the two classes are separable by an hy-
perplane. In the case where this property is not directly satisfied in the input
space, one is given the possibility to map instances into an intermediate feature
space where the classes are linearly separable. This intermediate space can ei-
ther be specified explicitly by hand-coded features, be defined implicitly with a
so-called kernel function, or be automatically learned. In both of the first cases,
it is the user’s responsibility to design the feature space. This can incur a huge
cost in terms of computational time or expert knowledge, especially with highly
dimensional input spaces, such as when dealing with images.
As for the third alternative, automatically learning the features with deep
architectures, i.e. architectures composed of multiple layers of nonlinear pro-
cessing, can be considered as a relevant choice. Indeed, some highly nonlinear
functions can be represented much more compactly in terms of number of param-
eters with deep architectures than with shallow ones (e.g. SVM). For example,
it has been proven that the parity function for n-bit inputs can be coded by
a feed-forward neural network with O(log n) hidden layers and O(n) neurons,
while a feed-forward neural network with only one hidden layer needs an expo-
nential number of the same neurons to perform the same task [1]. Moreover, in
the case of highly varying functions, learning algorithms entirely based on local
generalization are severely impacted by the curse of dimensionality [2]. Deep
architectures address this issue with the use of distributed representations and
as such may constitute a tractable alternative.
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2. v = input
h1
h2
Figure 1: The deep learning scheme: a greedy unsupervised layer-wise pre-
training stage followed by a supervised fine-tuning stage affecting all layers.
Unfortunately, training deep architectures is a difficult task and classical
methods that have proved effective when applied to shallow architectures are
not as efficient when adapted to deep architectures. Adding layers does not
necessarily lead to better solutions. For example, the more the number of layers
in a neural network, the lesser the impact of the back-propagation on the first
layers. The gradient descent then tends to get stuck in local minima or plateaus
[3], which is why practitioners have often preferred to limit neural networks to
one or two hidden layers.
This issue has been solved by introducing an unsupervised layer-wise pre-
training of deep architectures [3, 4]. More precisely, in a deep learning scheme
each layer is treated separately and successively trained in a greedy manner: once
the previous layers have been trained, a new layer is trained from the encoding
of the input data by the previous layers. Then, a supervised fine-tuning stage of
the whole network can be performed (see Fig. 1).
This paper aims at providing to the reader a better understanding of the
deep learning through a review of the literature and an emphasis of its key
properties. Section 2 details a widely used deep network model: the deep belief
network or stacked restricted Boltzmann machines. Other models found in deep
architectures are presented in Sect. 3, i.e. stacked auto-associators, deep kernel
machines and deep convolutional networks. Section 4 summarizes the main
results in the different application domains, points out the contributions of the
deep learning scheme and concludes the tutorial.
2 Deep learning with RBMs
2.1 Restricted Boltzmann Machines
Restricted Boltzmann Machines (RBMs) are at the intersection of several fields
of study and benefit from a rich theoretical framework [5, 6]. First, we will
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and Machine Learning. Bruges (Belgium), 27-29 April 2011, i6doc.com publ., ISBN 978-2-87419-044-5.
Available from http://www.i6doc.com/en/livre/?GCOI=28001100817300.
3. Figure 2: The RBM architecture with a visible (v) and a hidden (h) layers.
present them as a probabilistic model before showing how the neural network
equations arise naturally.
An RBM defines a probability distribution p on data vectors v as follows:
p(v) =
h
e−E(v,h)
u,g e−E(u,g)
. (1)
The variable v is the input vector and the variable h corresponds to unob-
served features [7] that can be thought of as hidden causes not available in the
original dataset. An RBM defines a joint probability on both the observed and
unobserved variables which are referred to as visible and hidden units respec-
tively (see Fig. 2). The distribution is then marginalized over the hidden units
to give a distribution over the visible units only. The probability distribution
is defined by an energy function E (RBMs are a special case of energy-based
models [8]), which is usually defined over couples (v, h) of binary vectors by:
E(v, h) = −
i
aivi −
j
bjhj −
i,j
wijvihj, (2)
with ai and bj the biases associated to the input variables vi and hidden variables
hj respectively and wij the weights of a pairwise interaction between them. In
accordance with (1), configurations (v, h) with a low energy are given a high
probability whereas a high energy corresponds to a low probability.
The energy function above is crafted to make the conditional probabilities
p(h|v) and p(v|h) tractable. The computation is done using the usual neural
network propagation rule (see Fig. 2) with:
p(v|h) =
i
p(vi|h) and p(vi = 1|h) = sigm
⎛
⎝aj +
j
hjwij
⎞
⎠ ,
p(h|v) =
j
p(hj|v) and p(hj = 1|v) = sigm bj +
i
viwij , (3)
where sigm(x) = 1/(1 + exp(−x)) is the logistic activation function.
The model with the energy function (2) defines a distribution over binary
vectors and, as such, is not suitable for continuous valued data. To address this
479
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and Machine Learning. Bruges (Belgium), 27-29 April 2011, i6doc.com publ., ISBN 978-2-87419-044-5.
Available from http://www.i6doc.com/en/livre/?GCOI=28001100817300.
4. issue, E can be appropriately modified to define the Gaussian-Bernoulli RBM
by including a quadratic term on the visible units [3]:
E(v, h) =
i
(vi − ai)2
2σ2
i
−
j
bjhj −
i,j
wij
vi
σi
hj,
where σi represents the variance of the input variable vi. Using this energy
function, the conditional probability p(h|v) is almost unchanged but p(v|h)
becomes a multivariate Gaussian with mean ai + σi j wijhj and a diagonal
covariance matrix:
p(vi = x|h) =
1
σi
√
2π
· e
−
x − ai − σi j wijhj
2
2σ2
i ,
p(hj = 1|v) = sigm bj +
i
vi
σi
wij . (4)
In a deep architecture using Gaussian-Bernoulli RBM, only the first layer
is real-valued whereas all the others have binary units. Other variations of the
energy function are given in [3, 9, 10] to address the issue of continuous valued
inputs.
2.2 Learning with RBMs and Contrastive Divergence
In order to train RBMs as a probabilistic model, the natural criterion to maxi-
mize is the log-likelihood. This can be done with gradient ascent from a training
set D likewise:
∂ log p(D)
∂wij
=
x∈D
∂ log p(x)
∂wij
=
x∈D
g
∂E(x, g)
∂wij
e−E(x,g)
g e−E(x,g)
−
x∈D
u g
∂E(u, g)
∂wij
e−E(u,g)
u g e−E(u,g)
,
= Edata
∂E(x, g)
∂wij
− Emodel
∂E(u, g)
∂wij
,
where the first term is the expectation of ∂E(x,g)
∂wij
when the input variables are set
to an input vector x and the hidden variables are sampled according to the condi-
tional distribution p(h|x). The second term is an expectation of ∂E(u,g)
∂wij
when u
and g are sampled according to the joint distribution of the RBM p(u, g) and is
intractable. It can however be approximated with a Markov chain Monte Carlo
algorithm such as Gibbs sampling: starting from any configuration (v0
, h0
), one
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5. samples ht
according to p(h|vt−1
) and vt
according to p(v|ht
) until the sample
(vt
, ht
) is distributed closely enough to the target distribution p(v, h).
In practice, the number of steps can be greatly reduced by starting the
Markov chain with a sample from the training dataset and assuming that the
model is not too far from the target distribution. This is the idea behind the
Contrastive Divergence (CD) learning algorithm [11]. Although the maximized
criterion is not the log-likelihood anymore, experimental results show that gra-
dient updates almost always improve the likelihood of the model [11]. Moreover,
the improvement to the likelihood tend to zero as the length of the chain in-
creases [12], an argument which supports running the chain for a few steps only.
Notice that the possibility to use only the sign of the CD update is explored in
the present special session [13].
2.3 From stacked RBMs to deep belief networks
In an RBM, the hidden variables are independent conditionally to the visible
variables, but they are not statistically independent. Stacking RBMs aims at
learning these dependencies with another RBM. The visible layer of each RBM of
the stack is set to the hidden layer of the previous RBM (see Fig. 3). Following
the deep learning scheme, the first RBM is trained from the input instances
and other RBMs are trained sequentially after that. Stacking RBMs increases a
bound on the log-likelihood [14], which supports the expectation to improve the
performance of the model by adding layers.
Figure 3: The stacked RBMs architecture.
A stacked RBMs architecture is a deep generative model. Patterns generated
from the top RBM can be propagated back to the input layer using only the
conditional probabilities as in a belief network. This setup is referred to as a
Deep Belief Network [4].
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6. Figure 4: The training scheme of an AA.
3 Other models and variations
3.1 Stacked Auto-Associators
Another module which can be stacked in order to train a deep neural network
in a greedy layer-wise manner is the Auto-Associator (AA) [15, 16].
An AA is a two-layers neural network. The first layer is the encoding layer
and the second is the decoding layer. The number of neurons in the decoding
layer is equal to the network’s input dimensionality. The goal of an AA is to
compute a code y of an input instance x from which x can be recovered with
high accuracy. This models a two-stage approximation to the identity function:
fdec(fenc(x)) = fdec(y) = ˆx x,
with fenc the function computed by the encoding layer and fdec the function
computed by the decoding layer (see Fig. 4).
An AA can be trained by applying standard back-propagation of error deriva-
tives. Depending on the nature of the input data, the loss function can either be
the squared error LSE for continuous values or the cross-entropy LCE for binary
vectors:
LSE(x, ˆx) =
i
(ˆxi − xi)2
,
LCE(x, ˆx) =
i
[xi log ˆxi + (1 − xi) log(1 − ˆxi)].
The AA training method approximates the CD method of the RBM [14].
Another important fact is that an AA with a nonlinear fenc differs from a PCA
as it is able to capture multimodal aspects of the input distribution [17].
Similarly to the parametrization in an RBM, the decoder’s weight matrix
Wdec can be set to the transpose of the encoder’s weight matrix, i.e. Wdec =
Wenc. In such a case, the AA is said to have tied weights. The advantage of
this constraint is to avoid undesirable effects of the training process, such as
encoding the identity function, i.e. fenc(x) = x. This useless result is possible
when the encoding dimensionality is not smaller than the input dimensionality.
An interesting variant of the AA is the Denoising Auto-Associator (DAA)
[18]. A DAA is an AA trained to reconstruct noisy inputs. To achieve this
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and Machine Learning. Bruges (Belgium), 27-29 April 2011, i6doc.com publ., ISBN 978-2-87419-044-5.
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7. Figure 5: The training scheme of a DAA. Noisy components are marked with a
cross.
goal, the instance fed to the network is not x but a corrupted version ˜x. After
training, if the network is able to compute a reconstruction ˆx of x with a small
loss, then it is admitted that the network has learned to remove the noise in the
data in addition to encode it in a different feature space (see Fig. 5).
Finally, a Stacked Auto-Associator (SAA) [3, 19, 18, 20] is a deep neural
network trained following the deep learning scheme: an unsupervised greedy
layer-wise pre-training before a fine-tuning supervised stage, as explained in
Sect. 2.3 (see also Fig. 1). Surprisingly, for d dimensional inputs and layers
of size k d, a SAA rarely learns the identity function [3]. In addition, it is
possible to use different regularization rules and the most successful results have
been reported with adding a sparsity constraint on the encoding unit activations
[20, 21, 22]. This leads to learning very different features (w.r.t RBM) in the
intermediate layers and the network performs a trade-off between reconstruction
loss and information content of the representation [21].
3.2 Deep Kernel Machines
The Multilayer Kernel Machine (MKM) [23] has been introduced as a way to
learn highly nonlinear functions with the iterative application of weakly nonlin-
ear kernel methods.
The authors use the Kernel Principal Component Analysis (KPCA) [24]
for the unsupervised greedy layer-wise pre-training stage of the deep learning
scheme. From this method, the + 1th
layer learns a new representation of the
output of the layer by extracting the n principal components of the projection
of the output of in the feature space induced by the kernel.
In order to lower as much as possible the dimensionality of the new rep-
resentation in each layer, the authors propose to apply a supervised strategy
devoted to selecting the best informative features among the ones extracted by
the KPCA. It can be summarized as follows:
1. rank the nl features according to their mutual information with the class
labels;
2. for different values of K and ml ∈ {1 . . . nl}, compute the classification
error rate of a K-NN classifier using only the ml most informative features
on a validation set;
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8. 3. the value of ml with which the classifier has reached the lowest error rate
determines the number of features to retain.
However, the main drawback of using KPCA as the building block of an MKM
lies in the fact that the feature selection process must be done separately and
thus requires a time-expensive cross validation stage. To get rid of this issue
when training an MKM it is proposed in this special session [25] to use a more
efficient kernel method, the Kernel Partial Least Squares (KPLS).
KPLS does not need cross validation to select the best informative features
but embeds this process in the projection strategy [26]. The features are ob-
tained iteratively, in a supervised manner. At each iteration j, KPLS selects the
jth
feature the most correlated with the class labels by solving an updated eigen-
problem. The eigenvalue λj of the extracted feature indicates the discriminative
importance of this feature. The number of features to extract, i.e. the number
of iterations to be performed by KPLS, is determined by a simple thresholding
of λj.
3.3 Deep Convolutional Networks
Convolutional networks are the first examples of deep architectures [27, 28] that
have successfully achieved a good generalization on visual inputs. They are the
best known method for digit recognition [29]. They can be seen as biologically
inspired architectures, imitating the processing of “simple” and “complex” corti-
cal cells which respectively extract orientations information (similar to a Gabor
filtering) and compositions of these orientations.
The main idea of convolutional networks is to combine local computations
(convolution of the signal with weight sharing units) and pooling. The convo-
lutions are intended to give translation invariance to the system, as the weights
depend only on spatial separation and not on spatial position. The pooling al-
lows to construct a more abstract set of features through nonlinear combination
of the previous level features, taking into account the local topology of the input
data. By alternating convolution layers and pooling layers, the network succes-
sively extracts and combines local features to construct a good representation of
the input. The connectivity of the convolutional networks, where each unit in a
convolution or a pooling layer is only connected to a small subset of the preceding
layer, allows to train networks with as much as 7 hidden layers. The supervised
learning is easily achieved, through an error gradient backpropagation.
On the one hand, convolutional framework has been applied to RBM and
DBN [10, 30, 31]. In [31] the authors derive a generative pooling strategy which
scales well with image size and they show that the intermediate representations
are more abstract in the higher layer (from edges in the lower layers to object
parts in the higher). On the other hand, the unsupervised pre-training stage of
deep learning have been applied to convolutional networks [32] and can greatly
reduce the number of labeled examples required. Furthermore, deep convolu-
tional networks with sparse regularization [33] yield very promising results for
difficult visual detection tasks, such as pedestrian detection.
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9. 4 Discussion
4.1 What are the applicative domains for deep learning?
Deep learning architectures express their full potential when dealing with highly
varying functions, requiring a high number of labeled samples to be captured by
shallow architectures. Unsupervised pre-training allows, in practice, to achieve
good generalization performance when the training set is of limited size by po-
sitioning the network in a region of the parameter space where the supervised
gradient descent is less likely to fall in a local minimum of the loss function.
Deep networks have been largely applied to visual classification databases such
as handwritten digits1
, object categories2 3 4
, pedestrian detection [33] or off-
road robot navigation [34], and also on acoustic signals to perform audio clas-
sification [35]. In natural language processing, a very interesting approach [36]
gives a proof that deep architectures can perform multi-task learning, giving
state-of-the-art results on difficult tasks like semantic role labeling. Deep archi-
tectures can also be applied to regression with Gaussian processes [37] and time
series prediction [38]. In the latter, the conditional RBM have given promising
results.
Another interesting application area is highly nonlinear data compression.
To reduce the dimensionality of an input instance, it is sufficient for a deep
architecture that the number of units in its last layer is smaller than its input
dimensionality. In practice, limiting the size of a neuron layer can promote in-
teresting nonlinear structure of the data. Moreover, adding layers to a neural
network can lead to learning more abstract features, from which input instances
can be coded with high accuracy in a more compact form. Reducing the di-
mensionality of data has been presented as one of the first application of deep
learning [39]. This approach is very efficient to perform semantic hashing on
text documents [22, 40], where the codes generated by the deepest layer are
used to build a hash table from a set of documents. Retrived documents are
those whose code differs only by a few bits from the query document code. A
similar approach for a large scale image database is presented in this special
session [41].
4.2 Open questions and future directions
A significant part of the ongoing research aims at improving the deep networks
building blocks For RBMs, several propositions have been made to use real-
valued units rather than binary ones either by integrating the covariance of the
visible units in the hidden units update [42] or by approximating real-valued
units by noisy rectified linear units [9, 10]. For AAs, the denoising criterion is
particularly investigated since it achieves very good results on visual classifica-
tion tasks [43].
1MNIST: http://yann.lecun.com/exdb/mnist/
2Caltech-101: http://www.vision.caltech.edu/Image_Datasets/Caltech101/
3NORB: http://www.cs.nyu.edu/~ylclab/data/norb-v1.0/
4CIFAR-10: http://www.cs.utoronto.ca/~kriz/cifar.html
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ESANN 2011 proceedings, European Symposium on Artificial Neural Networks, Computational Intelligence
and Machine Learning. Bruges (Belgium), 27-29 April 2011, i6doc.com publ., ISBN 978-2-87419-044-5.
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10. Because the construction of good intermediate representations is a crucial
part of deep learning, a meaningful approach is to study the response of the
individual units in each layer. An effective strategy is to find the input pattern
that maximizes the activation of a given unit, starting from a random input and
performing a gradient ascent [44].
A major interrogation underlying the deep learning scheme concerns the role
of the unsupervised pre-training. In [44], the authors argue that pre-training acts
as an unusual form of regularization. By selecting a region in the parameter space
which is not always better than a random one, pre-training systematically leads
to better generalization. The authors provide results showing that pre-training
does not act as an optimization procedure which selects the region of the pa-
rameter space where the basins of attraction are the deepest. Pre-training only
modifies the starting point of supervised training and the regularization effect
does not vanish when the number of data increases. Deep learning breaks down
the problem of optimizing lower layers given that the upper layers have not yet
been trained. Lower layers extract robust and disentangled representations of
the factors of variations (e.g. on images: translation, rotation, scaling), whereas
higher layers select and combine these representations. A fusion of the unsuper-
vised and supervised paradigms in one single training scheme is an interesting
way to explore.
Choosing the correct dimensions of a deep architecture is not an obvious
process and the results shown in [29] open new perspectives on this topic. A
convolution network with a random filter bank and with the correct nonlinearities
can achieve near state-of-the-art results when there is few training labeled data
(such as in the Caltech-101 dataset). It has been shown that the architecture of
convolutional network has a major influence on the performance and that it is
possible to achieve a very fast architecture selection using only random weights
and no time-consuming learning procedure [45]. This, along with the work of
[46], points toward new directions for answering the difficult question of how to
efficiently set the sizes of layers in deep networks.
4.3 Conclusion
The strength of deep architectures is to stack multiple layers of nonlinear pro-
cessing, a process which is well suited to capture highly varying functions with a
compact set of parameters. The deep learning scheme, based on a greedy layer-
wise unsupervised pre-training, allows to position deep networks in a parameter
space region where the supervised fine-tuning avoids local minima. Deep learn-
ing methods achieve very good accuracy, often the best one, for tasks where a
large set of data is available, even if only a small number of instances are la-
beled. This approach raises many theoretical and practical questions, which are
investigated by a growing and very active research community and casts a new
light on our understanding of neural networks and deep architectures.
486
ESANN 2011 proceedings, European Symposium on Artificial Neural Networks, Computational Intelligence
and Machine Learning. Bruges (Belgium), 27-29 April 2011, i6doc.com publ., ISBN 978-2-87419-044-5.
Available from http://www.i6doc.com/en/livre/?GCOI=28001100817300.
11. Acknowledgements
This work was supported by the French ANR as part of the ASAP project under
grant ANR_09_EMER_001_04.
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